PHILADELPHIA (USA TODAY) -- A 10-year-old Pennsylvania girl who underwent a double-lung transplant amid a national debate over the organ allocation process has undergone a second transplant after the first failed and is now taking some breaths on her own, the girl's parents said Friday.

Sarah Murnaghan's mother said the first set of lungs failed within hours after the June 12 transplant at Children's Hospital of Philadelphia and Sarah was placed on machines. She was placed back on the lung transplant list the night after her surgery and received a second set of lungs on June 15.

"We were told ... that she was going to die," the suburban Philadelphia girl's mother, Janet Murnaghan, said at a news conference Friday afternoon in explaining why Sarah's second transplant was not publicly disclosed. "We weren't prepared to live out her dying in public."

Sarah initially received lungs from an adult donor after her parents sued over national rules that place children behind adolescents and adults on the list for adult lungs.

Janet Murnaghan said Sarah's condition began to "spiral out of control" shortly after the first surgery. A second set of lungs was found and were transplanted though they were infected with pneumonia, making the surgery extra risky.

Sarah's mother said the second transplant was a success and the girl was able to take a few breaths on her own. She was placed back on a ventilator due to partial paralysis of her diaphragm, a complication of surgery that is not allowing her lungs to expand, her mother said.

She said Sarah is slated for surgery on Monday in an effort to repair her diaphragm.

"Her doctors continue to wean her from her ventilator, her last two chest tubes were removed today we are taking steps to prepare her for extubation again," Janet Murnaghan said. "We're not out of the woods, but Sarah's health is trending in the right direction."

The second set of lungs came from a donor 12 or older.

The failure of the first transplant is not uncommon. A 2005 University of Pennsylvania study found nearly 12% of lung transplants experienced what's called primary graft failure, where the organ almost immediately begins to fail.

But the timing - she received a second set of lungs just three days after her first - was narrow.

Of 5,081 lung transplants performed between 2010 and 2012, there were only seven retransplants within a week of the initial operation, according to the United Network for Organ Sharing, the private nonprofit group contracted by the government to manage the transplant list.

"I think this very clearly illustrates that the decision needs to be scientific and medical, rather than judicial," said Lawrence O. Gostin, a prominent health law professor at Georgetown University, who questioned the legal basis of the rulings. "UNOS was under pressure from the publicity surrounding this case and the court's decision. It is highly unusual to get two transplants within days."

According to UNOS, a graft failure does not automatically propel someone to the top of a waiting list, but it does affect your score. Sarah was regarded as an adult, given a score and that score would need to have been at the top of the list for her specific tissue and blood type to be eligible for the next set of lungs.

UNOS did not immediately return a message seeking comment.

Earlier this month, the Organ Procurement and Transplantation Network, which is overseen by UNOS, resisted making rule changes for children under 12 seeking lung transplants, but it created a special appeal and review system to hear such cases.

The meeting was prompted by the cases of Murnaghan and 11-year-old Javier Acosta of New York City that saw federal Judge Michael Baylson rule they should be eligible for adult lungs after U.S. Health and Human Services Secretary Kathleen Sebelius declined to intervene in such cases. Both children have end-stage cystic fibrosis, and Javier's brother died two years ago while on the waiting list.

Their families had challenged existing transplant policy that made children under 12 wait for pediatric lungs to become available or be offered lungs donated by adults after adolescents and adults on the waiting list had been considered.

The network said the new special review option will expire on July 1, 2014, unless the full board of directors votes to keep it in place.

Currently 1,663 people in the U.S. seeking a lung transplant. Twelve are between the ages of 6 and 10.